TSTP Solution File: SET580^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SET580^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n097.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:30:45 EDT 2014
% Result : Theorem 26.74s
% Output : Proof 26.74s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SET580^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n097.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:11:46 CDT 2014
% % CPUTime : 26.74
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0xcc6bd8>, <kernel.Type object at 0xcc6ab8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (Xx:a) (X:(a->Prop)) (Y:(a->Prop)), ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False))) of role conjecture named cBOOL_PROP_23_pme
% Conjecture to prove = (forall (Xx:a) (X:(a->Prop)) (Y:(a->Prop)), ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xx:a) (X:(a->Prop)) (Y:(a->Prop)), ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False)))']
% Parameter a:Type.
% Trying to prove (forall (Xx:a) (X:(a->Prop)) (Y:(a->Prop)), ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False)))
% Found conj2000:=(conj200 x):((and (X Xx)) ((Y Xx)->False))
% Found (conj200 x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found ((conj20 ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> ((conj2 B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (or_introl00 (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found ((or_introl0 ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))
% Found x2:(X Xx)
% Found (fun (x3:((Y Xx)->False))=> x2) as proof of (X Xx)
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of (((Y Xx)->False)->(X Xx))
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of ((X Xx)->(((Y Xx)->False)->(X Xx)))
% Found (and_rect00 (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (((and (X Xx)) ((Y Xx)->False))->(X Xx))
% Found False_rect00:=(False_rect0 (((X Xx)->False)->(X Xx))):(((X Xx)->False)->(X Xx))
% Found (False_rect0 (((X Xx)->False)->(X Xx))) as proof of (((X Xx)->False)->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) x3)) (((X Xx)->False)->(X Xx))) as proof of (((X Xx)->False)->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))) as proof of (((X Xx)->False)->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))) as proof of (((X Xx)->False)->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))) as proof of ((Y Xx)->(((X Xx)->False)->(X Xx)))
% Found (and_rect00 (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))) as proof of (((and (Y Xx)) ((X Xx)->False))->(X Xx))
% Found ((or_ind00 (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))) as proof of (X Xx)
% Found (((or_ind0 (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))) as proof of (X Xx)
% Found ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))))) as proof of (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))
% Found ((conj10 (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found (((conj1 ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found conj2000:=(conj200 x):((and (X Xx)) ((Y Xx)->False))
% Found (conj200 x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found ((conj20 ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> ((conj2 B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (or_introl00 (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found ((or_introl0 ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))
% Found x2:(X Xx)
% Found (fun (x3:((Y Xx)->False))=> x2) as proof of (X Xx)
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of (((Y Xx)->False)->(X Xx))
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of ((X Xx)->(((Y Xx)->False)->(X Xx)))
% Found (and_rect00 (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (((and (X Xx)) ((Y Xx)->False))->(X Xx))
% Found False_rect00:=(False_rect0 ((not (X Xx))->(X Xx))):((not (X Xx))->(X Xx))
% Found (False_rect0 ((not (X Xx))->(X Xx))) as proof of ((not (X Xx))->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) x3)) ((not (X Xx))->(X Xx))) as proof of ((not (X Xx))->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))) as proof of ((not (X Xx))->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))) as proof of ((not (X Xx))->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))) as proof of ((Y Xx)->((not (X Xx))->(X Xx)))
% Found (and_rect00 (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))) as proof of (((and (Y Xx)) (not (X Xx)))->(X Xx))
% Found ((or_ind00 (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))) as proof of (X Xx)
% Found (((or_ind0 (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))) as proof of (X Xx)
% Found ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))))) as proof of (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))
% Found ((conj10 (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found (((conj1 ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found (fun (x:(not (Y Xx)))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found (fun (x:(not (Y Xx)))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of ((not (Y Xx))->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx)))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x10:=(x1 x20):(X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x00:=(x0 x10):(X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x00:=(x0 x10):(X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x10:=(x1 x20):(X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x00:=(x0 x10):(X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found conj2000:=(conj200 x):((and (X Xx)) ((Y Xx)->False))
% Found (conj200 x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found ((conj20 ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> ((conj2 B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (or_introl00 (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found ((or_introl0 ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))
% Found x2:(X Xx)
% Found (fun (x3:((Y Xx)->False))=> x2) as proof of (X Xx)
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of (((Y Xx)->False)->(X Xx))
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of ((X Xx)->(((Y Xx)->False)->(X Xx)))
% Found (and_rect00 (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (((and (X Xx)) ((Y Xx)->False))->(X Xx))
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found False_rect00:=(False_rect0 (((X Xx)->False)->(X Xx))):(((X Xx)->False)->(X Xx))
% Found (False_rect0 (((X Xx)->False)->(X Xx))) as proof of (((X Xx)->False)->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) x3)) (((X Xx)->False)->(X Xx))) as proof of (((X Xx)->False)->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))) as proof of (((X Xx)->False)->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))) as proof of (((X Xx)->False)->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))) as proof of ((Y Xx)->(((X Xx)->False)->(X Xx)))
% Found (and_rect00 (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))) as proof of (((and (Y Xx)) ((X Xx)->False))->(X Xx))
% Found ((or_ind00 (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))) as proof of (X Xx)
% Found (((or_ind0 (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))) as proof of (X Xx)
% Found ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx)))))))) as proof of (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))
% Found ((conj10 (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found (((conj1 ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))
% Found (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x10:=(x1 x20):(X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found conj2000:=(conj200 x):((and (X Xx)) ((Y Xx)->False))
% Found (conj200 x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found ((conj20 ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> ((conj2 B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x) as proof of ((and (X Xx)) ((Y Xx)->False))
% Found (or_introl00 (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found ((or_introl0 ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))) as proof of ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))
% Found x2:(X Xx)
% Found (fun (x3:((Y Xx)->False))=> x2) as proof of (X Xx)
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of (((Y Xx)->False)->(X Xx))
% Found (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2) as proof of ((X Xx)->(((Y Xx)->False)->(X Xx)))
% Found (and_rect00 (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (X Xx)
% Found (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2))) as proof of (((and (X Xx)) ((Y Xx)->False))->(X Xx))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found False_rect00:=(False_rect0 ((not (X Xx))->(X Xx))):((not (X Xx))->(X Xx))
% Found (False_rect0 ((not (X Xx))->(X Xx))) as proof of ((not (X Xx))->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) x3)) ((not (X Xx))->(X Xx))) as proof of ((not (X Xx))->(X Xx))
% Found ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))) as proof of ((not (X Xx))->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))) as proof of ((not (X Xx))->(X Xx))
% Found (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))) as proof of ((Y Xx)->((not (X Xx))->(X Xx)))
% Found (and_rect00 (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))) as proof of (X Xx)
% Found ((and_rect0 (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))) as proof of (X Xx)
% Found (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))) as proof of (X Xx)
% Found (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))) as proof of (((and (Y Xx)) (not (X Xx)))->(X Xx))
% Found ((or_ind00 (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))) as proof of (X Xx)
% Found (((or_ind0 (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))) as proof of (X Xx)
% Found ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))))) as proof of (X Xx)
% Found (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx)))))))) as proof of (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))
% Found ((conj10 (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found (((conj1 ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found (fun (x:(not (Y Xx)))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx))
% Found (fun (x:(not (Y Xx)))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x2:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) ((not (X Xx))->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))) as proof of ((not (Y Xx))->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))) (X Xx)))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x00:=(x0 x10):(X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x00:=(x0 x10):(X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x10:=(x1 x20):(X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found (x1 x20) as proof of (X Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x00:=(x0 x10):(X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found (x0 x10) as proof of (X Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x10) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x00) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x4:((Y Xx)->False)
% Found (fun (x4:((Y Xx)->False))=> x4) as proof of (not (Y Xx))
% Found (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4) as proof of (((Y Xx)->False)->(not (Y Xx)))
% Found (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4) as proof of ((X Xx)->(((Y Xx)->False)->(not (Y Xx))))
% Found (and_rect10 (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)) as proof of (not (Y Xx))
% Found ((and_rect1 (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)) as proof of (not (Y Xx))
% Found (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)) as proof of (not (Y Xx))
% Found (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4))) as proof of (not (Y Xx))
% Found (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4))) as proof of (((and (X Xx)) ((Y Xx)->False))->(not (Y Xx)))
% Found x40:=(x4 x00):False
% Found (x4 x00) as proof of False
% Found (fun (x5:(Y Xx))=> (x4 x00)) as proof of False
% Found (fun (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)) as proof of (not (Y Xx))
% Found (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)) as proof of ((not (X Xx))->(not (Y Xx)))
% Found (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)) as proof of ((Y Xx)->((not (X Xx))->(not (Y Xx))))
% Found (and_rect10 (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))) as proof of (not (Y Xx))
% Found ((and_rect1 (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))) as proof of (not (Y Xx))
% Found (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))) as proof of (not (Y Xx))
% Found (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)))) as proof of (not (Y Xx))
% Found (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)))) as proof of (((and (Y Xx)) (not (X Xx)))->(not (Y Xx)))
% Found ((or_ind00 (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found (((or_ind0 (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found ((((fun (P:Prop) (x2:(((and (X Xx)) ((Y Xx)->False))->P)) (x3:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x2) x3) x10)) (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found ((((fun (P:Prop) (x2:(((and (X Xx)) ((Y Xx)->False))->P)) (x3:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x2) x3) (x1 x00))) (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found ((((fun (P:Prop) (x2:(((and (X Xx)) ((Y Xx)->False))->P)) (x3:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x2) x3) (x1 x00))) (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x4:((Y Xx)->False)
% Found (fun (x4:((Y Xx)->False))=> x4) as proof of (not (Y Xx))
% Found (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4) as proof of (((Y Xx)->False)->(not (Y Xx)))
% Found (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4) as proof of ((X Xx)->(((Y Xx)->False)->(not (Y Xx))))
% Found (and_rect10 (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)) as proof of (not (Y Xx))
% Found ((and_rect1 (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)) as proof of (not (Y Xx))
% Found (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)) as proof of (not (Y Xx))
% Found (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4))) as proof of (not (Y Xx))
% Found (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4))) as proof of (((and (X Xx)) ((Y Xx)->False))->(not (Y Xx)))
% Found x40:=(x4 x00):False
% Found (x4 x00) as proof of False
% Found (fun (x5:(Y Xx))=> (x4 x00)) as proof of False
% Found (fun (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)) as proof of (not (Y Xx))
% Found (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)) as proof of ((not (X Xx))->(not (Y Xx)))
% Found (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)) as proof of ((Y Xx)->((not (X Xx))->(not (Y Xx))))
% Found (and_rect10 (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))) as proof of (not (Y Xx))
% Found ((and_rect1 (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))) as proof of (not (Y Xx))
% Found (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))) as proof of (not (Y Xx))
% Found (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)))) as proof of (not (Y Xx))
% Found (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)))) as proof of (((and (Y Xx)) (not (X Xx)))->(not (Y Xx)))
% Found ((or_ind00 (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found (((or_ind0 (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found ((((fun (P:Prop) (x2:(((and (X Xx)) ((Y Xx)->False))->P)) (x3:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x2) x3) x10)) (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found ((((fun (P:Prop) (x2:(((and (X Xx)) ((Y Xx)->False))->P)) (x3:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x2) x3) (x1 x00))) (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00))))) as proof of (not (Y Xx))
% Found (fun (x1:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))))=> ((((fun (P:Prop) (x2:(((and (X Xx)) ((Y Xx)->False))->P)) (x3:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x2) x3) (x1 x00))) (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)))))) as proof of (not (Y Xx))
% Found (fun (x1:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))))=> ((((fun (P:Prop) (x2:(((and (X Xx)) ((Y Xx)->False))->P)) (x3:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x2) x3) (x1 x00))) (not (Y Xx))) (fun (x2:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x3:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x3) x2)) (not (Y Xx))) (fun (x3:(X Xx)) (x4:((Y Xx)->False))=> x4)))) (fun (x2:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x3:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x3) x2)) (not (Y Xx))) (fun (x3:(Y Xx)) (x4:(not (X Xx))) (x5:(Y Xx))=> (x4 x00)))))) as proof of (((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))->(not (Y Xx)))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x10:=(x1 x21):(X Xx)
% Found (x1 x21) as proof of (X Xx)
% Found (x1 x21) as proof of (X Xx)
% Found x20:=(x2 x11):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x50:=(x5 x10):False
% Found (x5 x10) as proof of False
% Found (fun (x5:((X Xx)->False))=> (x5 x10)) as proof of False
% Found (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)) as proof of (((X Xx)->False)->False)
% Found (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)) as proof of ((Y Xx)->(((X Xx)->False)->False))
% Found (and_rect10 (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))) as proof of False
% Found ((and_rect1 False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))) as proof of False
% Found (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))) as proof of False
% Found (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)))) as proof of False
% Found (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)))) as proof of (((and (Y Xx)) ((X Xx)->False))->False)
% Found x50:=(x5 x0):False
% Found (x5 x0) as proof of False
% Found (fun (x5:((Y Xx)->False))=> (x5 x0)) as proof of False
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of (((Y Xx)->False)->False)
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of ((X Xx)->(((Y Xx)->False)->False))
% Found (and_rect10 (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found ((and_rect1 False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of (((and (X Xx)) ((Y Xx)->False))->False)
% Found ((or_ind00 (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found (((or_ind0 False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x20)) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x10 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x10:=(x1 x00):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x10 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x11):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found x50:=(x5 x0):False
% Found (x5 x0) as proof of False
% Found (fun (x5:((Y Xx)->False))=> (x5 x0)) as proof of False
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of (((Y Xx)->False)->False)
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of ((X Xx)->(((Y Xx)->False)->False))
% Found (and_rect10 (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found ((and_rect1 False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of (((and (X Xx)) ((Y Xx)->False))->False)
% Found x50:=(x5 x10):False
% Found (x5 x10) as proof of False
% Found (fun (x5:((X Xx)->False))=> (x5 x10)) as proof of False
% Found (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)) as proof of (((X Xx)->False)->False)
% Found (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)) as proof of ((Y Xx)->(((X Xx)->False)->False))
% Found (and_rect10 (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))) as proof of False
% Found ((and_rect1 False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))) as proof of False
% Found (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))) as proof of False
% Found (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)))) as proof of False
% Found (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)))) as proof of (((and (Y Xx)) ((X Xx)->False))->False)
% Found ((or_ind00 (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found (((or_ind0 False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) x20)) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10))))) as proof of False
% Found (fun (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)))))) as proof of False
% Found (fun (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 x10)))))) as proof of (((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->False)
% Found x00:=(x0 x11):(X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20:=(x2 x10):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x20 as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x00:=(x0 x11):(X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found x10:=(x1 x01):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x01) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x1 x01) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x10:=(x1 x21):(X Xx)
% Found (x1 x21) as proof of (X Xx)
% Found (x1 x21) as proof of (X Xx)
% Found x20:=(x2 x11):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x50:=(x5 x00):False
% Found (x5 x00) as proof of False
% Found (fun (x5:(not (X Xx)))=> (x5 x00)) as proof of False
% Found (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00)) as proof of ((not (X Xx))->False)
% Found (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00)) as proof of ((Y Xx)->((not (X Xx))->False))
% Found (and_rect10 (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))) as proof of False
% Found ((and_rect1 False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))) as proof of False
% Found (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))) as proof of False
% Found (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00)))) as proof of False
% Found (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00)))) as proof of (((and (Y Xx)) (not (X Xx)))->False)
% Found x50:=(x5 x2):False
% Found (x5 x2) as proof of False
% Found (fun (x5:((Y Xx)->False))=> (x5 x2)) as proof of False
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2)) as proof of (((Y Xx)->False)->False)
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2)) as proof of ((X Xx)->(((Y Xx)->False)->False))
% Found (and_rect10 (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))) as proof of False
% Found ((and_rect1 False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))) as proof of False
% Found (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2)))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2)))) as proof of (((and (X Xx)) ((Y Xx)->False))->False)
% Found ((or_ind00 (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))))) as proof of False
% Found (((or_ind0 False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) x10)) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) (x1 x00))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) (x1 x00))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x2))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x00))))) as proof of False
% Found x50:=(x5 x10):False
% Found (x5 x10) as proof of False
% Found (fun (x5:(not (X Xx)))=> (x5 x10)) as proof of False
% Found (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)) as proof of ((not (X Xx))->False)
% Found (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)) as proof of ((Y Xx)->((not (X Xx))->False))
% Found (and_rect10 (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))) as proof of False
% Found ((and_rect1 False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))) as proof of False
% Found (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))) as proof of False
% Found (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)))) as proof of False
% Found (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)))) as proof of (((and (Y Xx)) (not (X Xx)))->False)
% Found x50:=(x5 x0):False
% Found (x5 x0) as proof of False
% Found (fun (x5:((Y Xx)->False))=> (x5 x0)) as proof of False
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of (((Y Xx)->False)->False)
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of ((X Xx)->(((Y Xx)->False)->False))
% Found (and_rect10 (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found ((and_rect1 False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of (((and (X Xx)) ((Y Xx)->False))->False)
% Found ((or_ind00 (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found (((or_ind0 False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) x20)) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found x00:=(x0 x11):(X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found x00:=(x0 x11):(X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found (x0 x11) as proof of (X Xx)
% Found x20:=(x2 x11):((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found (x2 x11) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))
% Found x50:=(x5 x0):False
% Found (x5 x0) as proof of False
% Found (fun (x5:((Y Xx)->False))=> (x5 x0)) as proof of False
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of (((Y Xx)->False)->False)
% Found (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)) as proof of ((X Xx)->(((Y Xx)->False)->False))
% Found (and_rect10 (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found ((and_rect1 False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of False
% Found (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0)))) as proof of (((and (X Xx)) ((Y Xx)->False))->False)
% Found x50:=(x5 x10):False
% Found (x5 x10) as proof of False
% Found (fun (x5:(not (X Xx)))=> (x5 x10)) as proof of False
% Found (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)) as proof of ((not (X Xx))->False)
% Found (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)) as proof of ((Y Xx)->((not (X Xx))->False))
% Found (and_rect10 (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))) as proof of False
% Found ((and_rect1 False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))) as proof of False
% Found (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))) as proof of False
% Found (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)))) as proof of False
% Found (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)))) as proof of (((and (Y Xx)) (not (X Xx)))->False)
% Found ((or_ind00 (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found (((or_ind0 False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) x20)) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10))))) as proof of False
% Found (fun (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)))))) as proof of False
% Found (fun (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx))))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) (not (X Xx)))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))) P) x3) x4) (x2 x10))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) (not (X Xx))))=> (((fun (P:Type) (x4:((Y Xx)->((not (X Xx))->P)))=> (((((and_rect (Y Xx)) (not (X Xx))) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:(not (X Xx)))=> (x5 x10)))))) as proof of (((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) (not (X Xx)))))->False)
% Found x2:(Y Xx)
% Found x2 as proof of (Y Xx)
% Found x0:(Y Xx)
% Found x0 as proof of (Y Xx)
% Found x60:=(x6 x3):False
% Found (x6 x3) as proof of False
% Found (fun (x6:((X Xx)->False))=> (x6 x3)) as proof of False
% Found (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)) as proof of (((X Xx)->False)->False)
% Found (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)) as proof of ((Y Xx)->(((X Xx)->False)->False))
% Found (and_rect10 (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))) as proof of False
% Found ((and_rect1 False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))) as proof of False
% Found (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))) as proof of False
% Found (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))) as proof of False
% Found (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))) as proof of (((and (Y Xx)) ((X Xx)->False))->False)
% Found x60:=(x6 x0):False
% Found (x6 x0) as proof of False
% Found (fun (x6:((Y Xx)->False))=> (x6 x0)) as proof of False
% Found (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0)) as proof of (((Y Xx)->False)->False)
% Found (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0)) as proof of ((X Xx)->(((Y Xx)->False)->False))
% Found (and_rect10 (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))) as proof of False
% Found ((and_rect1 False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))) as proof of False
% Found (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))) as proof of False
% Found (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0)))) as proof of False
% Found (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0)))) as proof of (((and (X Xx)) ((Y Xx)->False))->False)
% Found ((or_ind00 (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))) as proof of False
% Found (((or_ind0 False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))) as proof of False
% Found ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) x20)) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))) as proof of False
% Found ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))) as proof of False
% Found (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))) as proof of False
% Found (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))) as proof of ((X Xx)->False)
% Found ((conj10 x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))) as proof of ((and (Y Xx)) ((X Xx)->False))
% Found (((conj1 ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))) as proof of ((and (Y Xx)) ((X Xx)->False))
% Found ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))) as proof of ((and (Y Xx)) ((X Xx)->False))
% Found ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))) as proof of ((and (Y Xx)) ((X Xx)->False))
% Found (or_intror00 ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found ((or_intror0 ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))) as proof of ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))
% Found ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))) as proof of False
% Found (fun (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))))))))))) as proof of False
% Found (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))))))))))) as proof of (((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->False)
% Found (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))))))))))) as proof of ((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->False))
% Found (and_rect00 (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))) as proof of False
% Found ((and_rect0 False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))) as proof of False
% Found (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))) as proof of False
% Found (fun (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))))))))))))) as proof of False
% Found (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))))))))))))) as proof of ((Y Xx)->False)
% Found (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3))))))))))))))))) as proof of (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))
% Found ((conj00 (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))))) as proof of ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False))
% Found (((conj0 (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))))) as proof of ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False))
% Found ((((conj (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))) (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))))) as proof of ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False))
% Found (fun (Y:(a->Prop))=> ((((conj (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))) (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))))) as proof of ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False))
% Found (fun (X:(a->Prop)) (Y:(a->Prop))=> ((((conj (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))) (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))))) as proof of (forall (Y:(a->Prop)), ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False)))
% Found (fun (Xx:a) (X:(a->Prop)) (Y:(a->Prop))=> ((((conj (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))) (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))))) as proof of (forall (X:(a->Prop)) (Y:(a->Prop)), ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False)))
% Found (fun (Xx:a) (X:(a->Prop)) (Y:(a->Prop))=> ((((conj (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))) (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x))))))) as proof of (forall (Xx:a) (X:(a->Prop)) (Y:(a->Prop)), ((iff ((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) ((Y Xx)->False)))
% Got proof (fun (Xx:a) (X:(a->Prop)) (Y:(a->Prop))=> ((((conj (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))) (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))))))
% Time elapsed = 26.124721s
% node=4868 cost=1911.000000 depth=39
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (Xx:a) (X:(a->Prop)) (Y:(a->Prop))=> ((((conj (((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))->((Y Xx)->False))) (((Y Xx)->False)->((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx)))) (fun (x:((iff ((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))) (X Xx))) (x0:(Y Xx))=> (((fun (P:Type) (x1:((((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))->(((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))->P)))=> (((((and_rect (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) P) x1) x)) False) (fun (x1:(((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) (x2:((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))))=> ((((fun (P:Prop) (x3:(((and (X Xx)) ((Y Xx)->False))->P)) (x4:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x3) x4) (x2 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))) False) (fun (x3:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x4:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x4) x3)) False) (fun (x4:(X Xx)) (x5:((Y Xx)->False))=> (x5 x0))))) (fun (x3:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x4:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x4) x3)) False) (fun (x4:(Y Xx)) (x5:((X Xx)->False))=> (x5 (x1 (((or_intror ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) ((((conj (Y Xx)) ((X Xx)->False)) x0) (fun (x3:(X Xx))=> ((((fun (P:Prop) (x4:(((and (X Xx)) ((Y Xx)->False))->P)) (x5:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x4) x5) (x2 x3))) False) (fun (x4:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x5:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x5) x4)) False) (fun (x5:(X Xx)) (x6:((Y Xx)->False))=> (x6 x0))))) (fun (x4:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x5:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x5) x4)) False) (fun (x5:(Y Xx)) (x6:((X Xx)->False))=> (x6 x3)))))))))))))))))) (fun (x:((Y Xx)->False))=> ((((conj (((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False)))->(X Xx))) ((X Xx)->((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))) (fun (x0:((or ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))))=> ((((fun (P:Prop) (x1:(((and (X Xx)) ((Y Xx)->False))->P)) (x2:(((and (Y Xx)) ((X Xx)->False))->P))=> ((((((or_ind ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) P) x1) x2) x0)) (X Xx)) (fun (x1:((and (X Xx)) ((Y Xx)->False)))=> (((fun (P:Type) (x2:((X Xx)->(((Y Xx)->False)->P)))=> (((((and_rect (X Xx)) ((Y Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(X Xx)) (x3:((Y Xx)->False))=> x2)))) (fun (x1:((and (Y Xx)) ((X Xx)->False)))=> (((fun (P:Type) (x2:((Y Xx)->(((X Xx)->False)->P)))=> (((((and_rect (Y Xx)) ((X Xx)->False)) P) x2) x1)) (X Xx)) (fun (x2:(Y Xx))=> ((fun (P:Type)=> ((False_rect P) (x x2))) (((X Xx)->False)->(X Xx))))))))) (fun (x0:(X Xx))=> (((or_introl ((and (X Xx)) ((Y Xx)->False))) ((and (Y Xx)) ((X Xx)->False))) (((fun (B:Prop)=> (((conj (X Xx)) B) x0)) ((Y Xx)->False)) x)))))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------